Method for determining the distribution volume of a blood component during an extracorporeal blood treatment and device for carrying out the method

ABSTRACT

The invention relates to a method for determining the volume of distribution of a blood component in the body of a living organism, especially the volume of distribution of urea, during an extracorporeal blood treatment. According to this method, the blood to be treated flows through the blood chamber ( 3 ) of a dialysis machine ( 1 ) in an extracorporeal circuit, said dialysis machine being divided into said blood chamber and a dialysing liquid chamber ( 4 ) by a semipermeable membrane ( 2 ). Dialysing liquid flows through the dialysing liquid chamber of the dialysis machine in a dialysing liquid channel. The method is based on the determination of the temporal change in the concentration of the blood component in the blood upstream of the dialysis machine using the temporal variation in a physical or chemical characteristic of the dialysing liquid upstream and downstream of the dialysis machine and the determination of the volume of distribution of the substance in the body of a living organism using the temporal variation in the concentration of the blood component in the blood. The invention also relates to a device for the extracorporeal blood treatment, comprising a device for determining the volume of distribution of a blood component in the body of a living organism.

The present invention relates to a method for determining thedistribution volume of a blood component in the body of an organism,particularly the urea distribution volume, during an extracorporealblood treatment. In addition, the present invention relates to anapparatus for determining the distribution volume of a blood componentin the body of an organism during an extracorporeal blood treatment inconjunction with a device for the extracorporeal blood treatment.

An essential task of the human kidneys is the separation of substances,usually eliminated with urine, from the blood, and the regulation of thewater and electrolyte excretion. Hemodialysis represents a treatmentmethod to compensate for dysfunctions of the kidneys with respect to theremoval of substances usually eliminated with urine, and the adjustmentof the electrolyte concentration in the blood.

During hemodialysis, the blood is conducted in an extracorporeal circuitthrough the blood chamber of a dialyzer, the blood chamber beingseparated from a dialyzing-fluid chamber by a semipermeable membrane. Adialyzing fluid containing the blood electrolytes in a specificconcentration flows through the dialyzing-fluid chamber. The substanceconcentration (cd) of the dialyzing fluid corresponds to theconcentration of the blood of a healthy individual. During thetreatment, the blood of the patient and the dialyzing fluid areconducted past both sides of the membrane, generally in counterflow witha predefined flow rate(Qb and Qd, respectively). The substances usuallyeliminated with urine diffuse through the membrane from the bloodchamber into the chamber for dialyzing fluid, while at the same time,electrolytes present in the blood and in the dialyzing fluid diffusefrom the chamber of higher concentration to the chamber of lowerconcentration. The substance exchange can be additionally influenced byapplying a trans-membrane pressure.

To permit optimization of the blood-treatment process, the determinationof parameters for the hemodialysis during the extracorporeal bloodtreatment (in-vivo) is necessary. Of interest is the value for theexchange efficiency of the dialyzer, which is represented by theso-called “clearance” or “dialysance D”.

Designated as clearance for a specific substance K is that virtual(calculated) blood volume which is completely freed of a specificsubstance per minute under defined conditions in the dialyzer. Thedialysance D is a further concept for determining the performance of adialyzer, in which the concentration of the eliminated substance in thedialyzing fluid is taken into account. In addition to these parametersfor describing the performance of the dialyzer, other parameters arealso important, such as the values for the aqueous component of theblood, the blood volume and the blood input concentration, etc.

The mathematical quantification, using measuring techniques, of theblood-purification process and the determination of the aforesaidparameters of the dialysis are relatively complex. With respect to thecomputational fundamentals, reference is made to J. A. Sargent, F. A.Gotch: “Principles and Biophysics of Dialysis” in: Replacement of RenalFunction by Dialysis, C. Jacobs, C. M. Kjellstrand, K. M. Koch, J. F.Winchester (editor), Kluwer Academie Publisher, Dordrecht, 1996.

The dialysance, i.e. the clearance can be determined as follows for agiven electrolyte, e.g. sodium, at an ultra-filtration rate of zero. Thedialysance D is equal to the relationship between the mass transport onthe blood side for this electrolyte (Q_(b)×(cbi−cbo)) and theconcentration difference of this electrolyte between the blood and thedialyzing fluid at the respective input of the dialyzer (cbi−cdi).

$\begin{matrix}{D = {{Qb} \cdot \frac{{cbi} - {cbo}}{{cbi} - {cdi}}}} & (1)\end{matrix}$

For reasons of mass balance, the following is applicable:Qb·(cbi−cbo)=−Qd·(cdi−cdo)  (2)Following from the two equations (1) and (2) indicated above is:

$\begin{matrix}{D = {{- {Qd}} \cdot \frac{{cdi} - {cdo}}{{cbi} - {cdi}}}} & (3)\end{matrix}$

In this context, in (1) through (3):

Qb=effective flow of blood

Qd=flow of dialyzing fluid

cb=substance concentration in the blood

cd=substance concentration in the dialyzing fluid

i=input of the dialyzer

o=output of the dialyzer

The effective blood flow is the flow of the blood component in which thesubstances to be removed are dissolved, i.e. it relates to the (aqueous)solution volume for this substance. Depending on the substance, it canbe the plasma water flow or the blood serum flow, i.e. the entire watercontent in the whole blood. If the whole-blood flow Q_(Vb) isascertained, then Qb can be determined from Q_(Vb) using a constantfactor.

In the event that the ultrafiltration rate Qf is not equal to zero,dialysance D is calculated as follows:

$\begin{matrix}{D = {{\left\lbrack {{Qd}\frac{{cdo} - {cdi}}{{cbi} - {cdi}}} \right\rbrack \cdot \left\lbrack {1 - \frac{Qf}{Qb}} \right\rbrack} + {Qf}}} & \left( {4a} \right)\end{matrix}$

The diffusive component of the dialysance D_(diff) is then calculated asfollows:

$\begin{matrix}{D_{diff} = {\left\lbrack {{Qd}\frac{{cdo} - {cdi}}{{cbi} - {cdi}}} \right\rbrack \cdot \left\lbrack {1 - \frac{Qf}{Qb}} \right\rbrack}} & \left( {4b} \right)\end{matrix}$

For ionic substances, the Gibb's Donnan coefficient must be taken intoaccount for the blood input concentration. For this, reference is madeto the article by Sargent and Gotch cited above. For the sake ofsimplicity, this correction factor is omitted in the following.

The German patent DE 39 38 662 C2 (EP 0 428 927 A1) describes a methodfor the in-vivo determination of parameters for the hemodialysis, inwhich the dialysate-electrolyte transfer is in each case measured fortwo different dialysate input concentrations. Assuming that the bloodinput concentration is constant, according to the known method, thedialysance is determined in that the difference is determined betweenthe differences of the dialyzing fluid ion concentration at the inputside and the output side of the dialyzer at the instant of the first andsecond measurement, this is divided by the difference of the dialyzingfluid ion concentration at the input side at the instant of the firstmeasurement and of the second measurement and is multiplied by thedialyzing-fluid flow.

To be able to make a statement about the dialyzing dosage for thehemodialysis, the so-called “Kt/V” parameter is of particular interest.To calculate this parameter, the product of the clearance K and thetreatment time t is formed, and is divided by the distribution volume Vof the substance to be removed, usually urea.

The treatment time is predefined and therefore known. The clearance forthe type of dialyzer used can be gathered from tables, or else can beascertained online (DE 39 38 662 C2). In principle, the distributionvolume of a substance can be determined using a normal dilutionmeasurement in which an exactly measured marker fluid is injected intothe patient and its uniform concentration in the blood is measured aftera sufficient distribution time. However, this proves to be too costlyfor a routine process which must be used, for example, three times perweek.

Therefore, the distribution volume V is usually ascertained withempirical estimation formulas, into which parameters are entered such asthe body size and the weight of the patient to be treated. The valueascertained for V is admittedly very imprecise.

A method is known from WO 98/55166 for determining the mass of aconstituent such as urea in the blood, in which the concentration of theconstituent in the dialyzing fluid is measured downstream of thedialyzer during the treatment. The mass of the constituent is determinedfrom the change in the concentration as a function of time. Thedistribution volume should be calculated from the mass of theconstituent. It is disadvantageous that the distribution volume is notdetermined continually, but rather only at the end of a treatmentsegment.

The object of the present invention is to specify a method which allowsrapid and automated determination of the distribution volume of a bloodcomponent in the body of an organism during an extracorporeal bloodtreatment. A further objective underlying the present invention is toprovide an apparatus for determining the distribution volume of a bloodcomponent in the body of an organism.

This objective is achieved according to the present invention by thefeatures specified in Patent Claims 1 and 10, respectively.

Determination of the distribution volume of a blood component in thebody of an organism during an extracorporeal blood treatment is based onthe change in a physical or chemical characteristic of the dialyzingfluid in the dialyzing-fluid path during the blood treatment and themeasurement of the physical or chemical characteristic of the dialyzingfluid downstream of the dialyzer. The physical or chemicalcharacteristic of the dialyzing fluid is altered in the dialyzing-fluidpath upstream from the dialyzer. In this context, the physical orchemical characteristic should be adjusted to physiologically tenablevalues.

If the change in the characteristic upstream of the dialyzer is known,it is possible to dispense with this measurement. Otherwise thecharacteristic is measured not only downstream, but also upstream of thedialyzer.

The change in the concentration of the blood component in the blood as afunction of time is determined from the physical or chemicalcharacteristic of the dialyzing fluid downstream of the dialyzer. Thedistribution volume of the substance in the body of an organism is theninferred from the change in the concentration of the blood component inthe blood over time.

The physical or chemical characteristic of the dialyzing fluid upstreamand downstream of the dialyzer is advantageously the concentration of asubstance in the dialyzing fluid upstream and downstream of the dialyzer(dialyzing fluid input concentration and output concentration cdi, cdo).A deviation in the dialyzing fluid input concentration from the bloodinput concentration cbi leads to a change in the blood inputconcentration cbi at the dialyzer, since the measured substance shiftsto or from the blood side. The distribution volume of this substance inthe blood is then inferred from the change in the blood inputconcentration as a function of time.

To determine the distribution volume of sodium in the blood, preferablythe conductivity of the dialyzing fluid is measured as a physical orchemical characteristic. The known conductivity sensors can be used forthis purpose.

The urea distribution volume can be inferred from the sodiumdistribution volume, since the urea distribution volume correspondsessentially to the sodium distribution volume.

After the urea distribution volume is determined, the so-called “Kt/V”parameter can be calculated, in doing which the clearance K can eitherbe ascertained according to the method known from DE 39 38 662 C2, orgathered from corresponding tables for the individual types of dialyzer.

In calculating the distribution volume V, the starting point isinitially the following mass balance equation:

$\begin{matrix}{{{\int_{t}^{t + {\Delta\; t}}{{Qd}*{{cdi}\left( t^{\prime} \right)}\ {\mathbb{d}t^{\prime}}}} - {\int_{t}^{t + {\Delta\; t}}{\left( {{Qd} + {Qf}} \right)*{{cdo}\left( t^{\prime} \right)}\ {\mathbb{d}t^{\prime}}}}} = {{{V\left( {t + {\Delta\; t}} \right)}*{{cbi}\left( {t + {\Delta\; t}} \right)}} - {{V(t)}*{{cbi}(t)}}}} & (5)\end{matrix}$

Equation (5) represents how the blood concentration cbi changes on thebasis of the shift of substances into or out of the blood. If equation(5) is divided by Δt and the limiting value Δt→∞ is then considered,then the integral mass balance according to equation (5) is convertedinto a differential mass balance:

$\begin{matrix}{{{{Qd}*{{cdi}(t)}} - {\left( {{Qd} + {Qf}} \right)*{{cdo}(t)}}} = {{{{cbi}(i)}\frac{\mathbb{d}{V(t)}}{\mathbb{d}t}} - {{V(t)}\frac{\mathbb{d}{{cbi}(t)}}{\mathbb{d}t}}}} & (6)\end{matrix}$

Solved according to dcbi(t)/dt and with dV(t)/dt=−Qf, this yieldsequation (7):

$\begin{matrix}{\frac{\mathbb{d}{cbi}}{\mathbb{d}t} = \frac{{{Qd}*{{cdi}(t)}} - {\left( {{Qd} + {Qf}} \right)*{{cdo}(t)}} + {{Qf}*{{cbi}(t)}}}{V(t)}} & (7)\end{matrix}$

Equation (7) represents the basis for the continuing considerations, itbeing assumed that the time profile of cdi(t) leads to a change ofcbi(t), and the measuring time is conditional upon a sufficient mixturein the blood of the patient.

Equation (7) can be evaluated in widely varying forms. If one assumescdi(t)=const, as well as cdo(t)≈const and cbi(t)≈const during themeasuring phase, which is well fulfilled for the case of a concentrationgradient, changing only insignificantly during the measuring time,between the two fluids (i.e. the numerator in (7) changes onlyinsignificantly), then applicable for the period of time t to t+Δt is:

$\begin{matrix}{{V(t)} = \frac{\left( {{{Qd}*{{cdi}(t)}} - {\left( {{Qd} + {Qf}} \right)*{{cdo}(t)}} + {{Qf}*{{cbi}(t)}}} \right)\Delta\; t}{{{cbi}\left( {t + {\Delta\; t}} \right)} - {{cbi}(t)}}} & (8)\end{matrix}$

The physical or chemical characteristic of the dialyzing fluid upstreamof the dialyzer is preferably increased abruptly from an original valueto a predefined value, to then be abruptly reduced to a predefinedvalue, whereupon the original value is set again. If the value by whichthe characteristic is reduced is twice as large as the value by whichthe characteristic is increased, and the time interval in which thecharacteristic is increased is equal to the time interval in which thecharacteristic is reduced, then a symmetrical time profile is presentwhich simplifies the evaluation, since the increase in thecharacteristic is offset by its decrease. In order not to have to feedto or remove from the patient unnecessary amounts of, for example,sodium during the treatment, the initial value of the characteristic inthe dialyzing fluid, which is altered during the measurement, shouldcorrespond to the value in the blood.

In the event of unsymmetrical pulses for the two rectangular profiles,the change of the concentration in the blood as a function of time canbe exactly calculated by forming a relationship between integralsurfaces.

Determining the distribution volume is advantageously even furthersimplified because during the measurement, the volume of the dialyzingfluid flowing into the dialyzer is equal to the volume of fluid flowingout of the dialyzer. This can be accomplished using the familiarbalancing devices. However, it is also possible to ascertain thedistribution volume during a continuing ultrafiltration of the blood.

The distribution volume of a blood component in the body of an organismcan then also be determined without explicitly ascertaining the changein the concentration of the component in the blood as a function oftime.

An exemplary embodiment of a hemodialysis device having an apparatus fordetermining the urea distribution volume is further described in thefollowing with reference to the drawing, in which:

FIG. 1 shows a simplified schematic representation of a hemodialysisdevice having the apparatus for determining the urea distributionvolume; and

FIG. 2 shows the time profile of the dialyzing-fluid input and outputconcentration.

The apparatus for determining the urea distribution volume can form aseparate subassembly. However, it can also be a component of ahemodialysis device, particularly since some components of the apparatusfor determining the urea distribution volume are already present in theknown dialyzers. In the following, the apparatus for determining theurea distribution volume is described together with the essentialcomponents of the dialyzer.

The hemodialysis device has a dialyzer 1 which is separated by asemi-permeable membrane 2 into a blood chamber 3 and a dialyzing-fluidchamber 4. The inlet of the blood chamber is connected to one end of ablood feed line 5 into which a blood pump 6 is switched, while theoutlet of blood chamber 3 is connected to the one end of a blooddischarge line 7 into which a drip chamber 8 is switched.

The dialyzing-fluid system of the hemodialysis device includes a device9 for preparing the dialyzing fluid, with which different compositionsof the dialyzing fluid (electrolyte dose) can be preselected.Preparation device 9 has a device 17 for altering the substanceconcentration of the dialyzing fluid, preferably the sodiumconcentration. A balancing device is also provided which includes twoparallel-connected balance chambers that are each subdivided into twobalance-chamber halves. For the sake of greater clarity, only the twobalance-chamber halves of one balance chamber are shown here.Preparation device 9 is connected to the inlet of first chamber half 11a of balancing device 11 via first section 10 a of a dialyzing-fluidfeed line 10. Second section 10 b of dialyzing-fluid feed line 10connects the outlet of first balancing-chamber half 11 a to the inlet ofdialyzing-fluid chamber 4. The outlet of dialyzing-fluid chamber 4 isconnected via first section 12 a of a dialyzing-fluid discharge line 12to the inlet of second balancing-chamber half 11 b. A dialyzing-fluidpump 13 is switched into first section 12 a of dialyzing-fluid dischargeline 12. The outlet of second balancing-chamber half 11 b is connectedto a drain 14 via second section 12 b of dialyzing-fluid discharge line12. Upstream of dialyzing-fluid pump 13, an ultrafiltrate line 15branches off from dialyzing-fluid discharge line 12 and likewise leadsto drain 14. An ultrafiltration pump 16 is switched into ultrafiltrateline 15.

The hemodialysis device also includes a central control unit 18 that isconnected via control lines 19 through 22 to blood pump 6,dialyzing-fluid pump 13, ultrafiltration pump 16 and device 17 foraltering the sodium concentration of the dialyzing fluid.

During the dialysis treatment, the blood of the patient flows throughblood chamber 3, and the dialyzing fluid flows through dialyzing-fluidchamber 4 of dialyzer 1. Since balancing device 11 is switched into thedialyzing-fluid path, only so much dialyzing fluid can flow in viadialyzing-fluid feed line 10 as can flow off via dialyzing-fluiddischarge line 12. Fluid can be withdrawn from the patient usingultrafiltration pump 16, the desired ultrafiltration rate beingpredetermined by the control unit.

Measuring devices 23, 24, respectively, are arranged in feed line 10 anddischarge line 12 upstream and downstream of dialyzer 1 for determiningthe substance concentration of the dialyzing fluid at the input ofdialyzer 1 (dialyzing-fluid input concentration cdi) and the substanceconcentration of the dialyzing fluid at the output of the dialyzer(dialyzing-fluid output concentration cdo). Measuring devices 23, 24 fordetermining the dialyzing-fluid input and output concentration haveconductivity sensors which preferably measure the temperature-correctedconductivity of the dialyzing fluid and thus especially the Naconcentration. Instead of conductivity sensors, optical or othersensors, e.g. enzyme sensors, can also be arranged in thedialyzing-fluid path for measuring the dialyzing-fluid input and outputconcentration.

Arithmetic and evaluation unit 29 is connected via a data line 32 tocontrol unit 18 in order to be able to retrieve flow rates Qb, Qd forblood and dialyzing-fluid pumps 6, 13.

Measuring devices 23, 24 are connected via data lines 25, 26 to a memoryunit 27. Memory unit 27 receives the measured values of sensors andstores them in chronological sequence. The measured values are suppliedvia a data line 28 to an arithmetic and evaluation unit 29 which, in adigital computer (microprocessor), determines the urea distributionvolume from the data obtained. The urea distribution volume is displayedon a readout mechanism 30 that is connected via a data line 31 toarithmetic and evaluation unit 29.

The apparatus operates as follows for determining the urea distributionvolume:

At the beginning of the measurement, control unit 18 haltsultrafiltration pump 16, so that the ultrafiltration rate is equal to 0.The control unit predefines flow rates Qb and Qd for the flow of theblood and dialyzing fluid.

The dialyzing fluid flows through the dialyzing-fluid chamber with aflow rate Qd predefined by the speed of pump 13, and withdialyzing-fluid input concentration cdi which is set by device 17 andwhich is detected by measuring device 23 arranged upstream of thedialyzer. The dialyzing-fluid output concentration cdo appearing inresponse to the dialysis is detected by measuring device 24 arrangeddownstream of the dialyzer.

Device 17 adjusts a dialyzing-fluid input concentration cdi(t) which hasthe time profile shown in FIG. 2. Starting from a value cdi₀ which iscustomary for the dialysis treatment and which corresponds or at leastcomes close to the value cbi₀ of the sodium concentration in the bloodupstream of the dialyzer, the input concentration is increased to thevalue cdi₁ at point of time t₀. At point of time t₁, the inputconcentration is reduced to the value cdi₂, to then be set again to theoriginal value cdi₀ at point of time t₂.

FIG. 2 shows, in dotted lines, the time profile of dialyzing-fluidoutput concentration cdo(t) appearing downstream of the dialyzer.cdi₀=cdo₀ is for t<to. At the end of time interval t₀<t<t₁, a value cdo₁appears at the dialyzer output, while at the end of time intervalt₁<t<t₂, a value cd₀₂ appears at the dialyzer output. For t>t₂, thedialyzing-fluid output concentration again assumes the value of thedialyzing-fluid input concentration with sufficient accuracy. Thedialyzing-fluid input and output concentrations exhibit a symmetricaltime profile. The value by which the input concentration is reduced istwice as large as the value by which the input concentration isincreased. Time interval t₁−t₀ is equal to time interval t₂−t₁. The timeintervals are regulated such that in each case stable values ensue forcdo. Since the profile is symmetrical, the shift of electrolytes via themembrane of the dialyzer, caused by the first change, is compensated foragain.

While the dialyzing-fluid input concentration is changed, thedialyzing-fluid input and output concentrations cdi₀, cdo₀ within timeinterval t<t₀, cdi₁, cdo₁ within time interval t₀<t<t₁ and cdi₂, cdo₂within time interval t₁<t<t₂ are measured and stored in memory unit 27.In so doing, it is taken into account that the values for cdo aretime-displaced by a delay time t_(d) with respect to those of cdi.

Since the shift of electrolytes via the dialysis membrane, caused by thefirst change, is compensated for again in the symmetrical case, thefollowing applies:cdi₀=cbi₀=cbi₂  (9)points of time immediately prior to the change of cdi being designatedin each case with the subscript as t₀, t₁ and t₂.

The change as a function of time in the blood-input concentration Δcbiis calculated as follows:Δcbi=cbi ₁ −cbi ₀  (10)

On condition that an ultra-filtration rate of zero (Qf=0) is set, andassuming that dialysance D does not change during the measurement,arithmetic and evaluation unit 29 calculates Δcbi from the stored valuescdi₀, cdo₀, cdi₁, cdo₁ and cdi₂, cdo₂, as well as from the adjusteddialyzing-fluid flow rate Qd on the basis of the following equations:

$\begin{matrix}{D = \frac{\left\lbrack {\left( {{cdo}_{0} - {cdi}_{0}} \right) - \left( {{cdo}_{1} - {cdi}_{1}} \right)} \right\rbrack{Qd}}{\left( {{cbi}_{0} - {cdi}_{0}} \right) - \left( {{cbi}_{1} - {cdi}_{1}} \right)}} & (11) \\{D = \frac{\left\lbrack {\left( {{cdo}_{1} - {cdi}_{1}} \right) - \left( {{cdo}_{2} - {cdi}_{2}} \right)} \right\rbrack{Qd}}{\left( {{cbi}_{1} - {cdi}_{1}} \right) - \left( {{cbi}_{2} - {cdi}_{2}} \right)}} & (12) \\{D = \frac{\left\lbrack {\left( {{cdo}_{0} - {cdi}_{0}} \right) - \left( {{cdo}_{2} - {cdi}_{2}} \right)} \right\rbrack{Qd}}{\left( {{cbi}_{0} - {cdi}_{0}} \right) - \left( {{cbi}_{2} - {cdi}_{2}} \right)}} & (13)\end{matrix}$

In these three equations, only D and Δcbi are unknown. The arithmeticunit ascertains these parameters either from two equations hereof, fromaverage values of the respective combinations in pairs, or from avariation calculation which tries to fulfill all three equations as wellas possible. In the event D is already known, this can be utilized forfurther optimization.

After D and Δcbi are ascertained, sodium distribution volume V iscalculated in the arithmetic unit according to equation (8), whereΔcbi=cbi(t+Δt)−cbi(t) and Δt=t₁−t₂.

For this purpose, arithmetic and evaluation unit 29 reads out themeasured values for the dialyzing-fluid input and output concentrationscdi(t), cdo(t), stored during the measurement in their chronologicalsequence, from memory unit 27. The measuring signals of the conductivitysensors are advantageously sampled, the calculation being carried out bya digital computer.

Assuming that the ascertained sodium distribution volume is essentiallyequal to the urea distribution volume, the urea distribution volume isdetermined and displayed on readout mechanism 30. From the knownclearance K and treatment time t and the ascertained urea distributionvolume V, arithmetic and evaluation unit 29 calculates the “Kt/V”parameter which quantifies the dialyzing dosage. The “Kt/V” parameter islikewise displayed on readout mechanism 30.

For the aforesaid reasons, the change in the dialyzing-fluid inputconcentration as a function of time should be symmetrical. However, ifunsymmetrical pulses are used, it can no longer be assumed thatcbi₀=cbi₂. Applicable in this case is:cbi ₂ =cbi ₀ +Δcbi(I ₁ +I ₂)/I ₁  (14)

$\begin{matrix}{I_{1} = {\int_{0}^{t_{1}}{\left\lbrack {{{cdi}(t)} - {{cdo}\left( {t + {td}} \right)}} \right\rbrack\ {\mathbb{d}t}}}} & (15) \\{I_{2} = {\int_{t_{1}}^{t_{2}}{\left\lbrack {{{cdi}(t)} - {{cdo}\left( {t + {td}} \right)}} \right\rbrack\ {\mathbb{d}t}}}} & (16)\end{matrix}$

Delay time td is the time after which the dialyzing-fluid outputconcentration rises after the increase of the dialyzing-fluid inputconcentration. Delay time td is calculated from the measured timeprofile of input and output concentrations cdi(t) and cdo(t). It isevident from FIG. 2 that, for the case of a symmetrical profile of cdi,integral surfaces I₁ and I₂ are nearly identical, which means, asassumed before, cbi₂=cbi₀.

The sodium distribution volume is again calculated in arithmetic andevaluation unit 29 according to the equations (11) through (13), now,however, cbi₂=cbi₀+Δcbi(I₁+I₂)/I₁ being valid. The arithmetic andevaluation unit is provided with integrators for forming integrals I₁and I₂.

If ultrafiltration is carried on during the measurement, the sodiumdistribution volume can only be determined when the values cbi_(0,1,2)for the blood input concentration are known.

To this end, prior to measuring the distribution volume, the blood inputconcentration cbi can be determined as described in detail in the Germanpatent 39 38 662 C2, to which reference is specifically made. In thiscontext, it is sufficient to ascertain an average value for cbi_(0,1,2).

Arithmetic and evaluation unit 29 now determines Δcbi on the basis ofthe following equations:

$\begin{matrix}{D_{diff} = \frac{\begin{matrix}{{\left\lbrack {\left( {{cdo}_{0} - {cdi}_{0}} \right) - \left( {{cdo}_{1} - {cdi}_{1}} \right)} \right\rbrack{Qd}} +} \\{\left\lbrack {\left( {{cbi}_{1} - {cdo}_{1}} \right) - \left( {{cbi}_{0} - {cdo}_{0}} \right)} \right\rbrack{Qf}}\end{matrix}}{\left( {1 - \frac{Qf}{Qb}} \right)\left\lbrack {\left( {{cbi}_{0} - {cdi}_{0}} \right) - \left( {{cbi}_{1} - {cdi}_{1}} \right)} \right\rbrack}} & (17) \\{D_{diff} = \frac{\begin{matrix}{{\left\lbrack {\left( {{cdo}_{1} - {cdi}_{1}} \right) - \left( {{cdo}_{2} - {cdi}_{2}} \right)} \right\rbrack{Qd}} +} \\{\left\lbrack {\left( {{cbi}_{2} - {cdo}_{2}} \right) - \left( {{cbi}_{1} - {cdo}_{1}} \right)} \right\rbrack{Qf}}\end{matrix}}{\left( {1 - \frac{Qf}{Qb}} \right)\left\lbrack {\left( {{cbi}_{1} - {cdi}_{1}} \right) - \left( {{cbi}_{2} - {cdi}_{2}} \right)} \right\rbrack}} & (18) \\{D_{diff} = \frac{\begin{matrix}{{\left\lbrack {\left( {{cdo}_{0} - {cdi}_{0}} \right) - \left( {{cdo}_{2} - {cdi}_{2}} \right)} \right\rbrack{Qd}} +} \\{\left\lbrack {\left( {{cbi}_{2} - {cdo}_{2}} \right) - \left( {{cbi}_{0} - {cdo}_{0}} \right)} \right\rbrack{Qf}}\end{matrix}}{\left( {1 - \frac{Qf}{Qb}} \right)\left\lbrack {\left( {{cbi}_{0} - {cdi}_{0}} \right) - \left( {{cbi}_{2} - {cdi}_{2}} \right)} \right\rbrack}} & (19)\end{matrix}$

D_(diff) represents the diffusive component of the dialysance.

The change as a function of time in the blood-input concentration Δcbiis now determined in a similar manner as in the case of Q_(f)=0 fromequations (17) through (19). The sodium distribution volume is then inturn calculated according to equation (8). Arithmetic and evaluationunit 29 thereupon again determines the urea distribution volume from thesodium distribution volume.

However, distribution volume V of a blood component in the body of anorganism can also be determined in arithmetic and evaluation unit 29without explicitly ascertaining the change as a function of time in theconcentration of the component in the blood Δcbi. To this end, device 17again sets the profile, shown in FIG. 2, for the dialyzing-fluid inputconcentration cdi(t). The points of time “beginning”, “end of the highphase” and “end of the low phase” are again indexed with 0, 1 and 2,respectively.

Dialysance D can be calculated as follows from the dialyzing-fluid inputand output concentrations at points of time i, j:

$\begin{matrix}{D_{i,j} = {{\left( {1 - \frac{{cdo}_{i} - {cdo}_{j}}{{cdi}_{i} - {cdi}_{j}}} \right)\left( {{Qd} + {Qf}} \right)\mspace{31mu}\text{time~~index}\mspace{14mu} i} \neq j}} & (20)\end{matrix}$

The above equation is derived assuming that the plasma-sodium isconstant. However, this is not the case because of the salt transfer. Ifthis assumption is not made, then the dialysance is calculated asfollows:

$\begin{matrix}{D_{i,j} = {\frac{\begin{matrix}{{\left\lbrack {\left( {{cdo}_{i} - {cdi}_{i}} \right) - \left( {{cdo}_{j} - {cdi}_{j}} \right)} \right\rbrack{Qd}} +} \\{\left\lbrack {\left( {{cbi}_{j} - {cdo}_{j}} \right) - \left( {{cbi}_{i} - {cdo}_{i}} \right)} \right\rbrack{Qf}}\end{matrix}}{\left( {{cbi}_{i} - {cdi}_{i}} \right) - \left( {{cbi}_{j} - {cdi}_{j}} \right)} + {Qf}}} & (21)\end{matrix}$

Analogously, the diffusive component of dialysance D_(diff) for aconstant plasma-sodium concentration reads as follows:

$\begin{matrix}{D_{{{diff}\mspace{14mu} i},j} = \frac{{\left\lbrack {\left( {{cdo}_{i} - {cdi}_{i}} \right) - \left( {{cdo}_{j} - {cdi}_{j}} \right)} \right\rbrack{Qd}} + {\left( {{cdo}_{i} - {cdo}_{j}} \right){Qf}}}{\left( {1 - \frac{Qf}{Qb}} \right)\left\lbrack \left( {{cdi}_{j} - {cdi}_{i}} \right) \right\rbrack}} & (22)\end{matrix}$

If the assumption is dropped, the diffusive component of dialysanceD_(diff) is calculated as follows:

$\begin{matrix}{D_{{{diff}\mspace{14mu} i},j} = \frac{\begin{matrix}{{\left\lbrack {\left( {{cdo}_{i} - {cdi}_{i}} \right) - \left( {{cdo}_{j} - {cdi}_{j}} \right)} \right\rbrack{Qd}} +} \\{\left\lbrack {\left( {{cbi}_{j} - {cdo}_{j}} \right) - \left( {{cbi}_{i} - {cdo}_{i}} \right)} \right\rbrack{Qf}}\end{matrix}}{\left( {1 - \frac{Qf}{Qb}} \right)\left\lbrack {\left( {{cbi}_{i} - {cdi}_{i}} \right) - \left( {{cbi}_{j} - {cdi}_{j}} \right)} \right\rbrack}} & (23)\end{matrix}$

Experiments have shown that, for the step-index profile shown in FIG. 2,equations (20) and (22), respectively, are a good approximation forequations (21) and (23), respectively, for i=1 and j=2.

If the values for the dialysance, which take into account theelectrolyte transfer, are now compared to those resulting from aconstant blood input concentration cbi, then distribution volume V canbe determined.

To determine the distribution volume V, arithmetic and evaluation unit29 first of all calculates, from the stored measured values, valuesD_(0,1), D_(1,2) and D_(diff1,2) according to equations (20) and (22)for dialysance D and the diffusive component of the dialysance D_(diff).An ultra-filtration rate Qf of zero is preferably set when acquiring themeasurable quantities cdi and cdo.

After determining the above values, the arithmetic and evaluation unitthen calculates the distribution volume of the blood component accordingto the following equation:

$\begin{matrix}{{V\left( t_{1} \right)} = {\left( {\frac{D_{0,1}}{D_{1,2} - D_{0,1}} + 1} \right) \cdot \left( \frac{{D_{{{diff}\mspace{14mu} 1},2}\left( {t_{1} - t_{0}} \right)}\left( {{cdi}_{1} - {cbi}_{0}} \right)}{{cdi}_{1} - {cdi}_{0}} \right)}} & (24)\end{matrix}$

For a constant ultrafiltration rate, distribution volume V can becalculated for any points of time t as follows:V(t)=V(t ₁)+Qf(t ₁−1)

The concentration of the component in the blood cbi₀ (blood-inputconcentration) is determined beforehand according to equation (4a) or(4b). Namely, after the arithmetic and evaluation unit has determinedthe dialysance, the sought-after concentration cbi is the singleunknown.

The above equations show that it is not explicitly necessary todetermine the change in the blood-input concentration as a function oftime. It is sufficient to determine this variable at point of time t₀.

Equation (24) was derived assuming that the measurable quantities arerecorded only a few minutes after a change in the dialyzing-fluid inputconcentration, and a shift of electrolytes through the dialyzer membraneproportional to the time ensues. It was further assumed that therecirculation in the fistula of the patient can be disregarded. Toexpand the validity range as a function of time and to take into accountthe recirculation, it is also possible to allow for empiricallyascertained correction factors a₁ for D_(0,1), D_(1,2) and D_(diff1,2)in equation (24). The calculation is then carried out according to thefollowing equation:

$\begin{matrix}{{V\left( t_{1} \right)} = {\left( {\frac{a_{1}D_{0,1}}{{a_{2}D_{1,2}} - {a_{1}D_{0,1}}} + 1} \right) \cdot \left( \frac{a_{3}{D_{{{diff}\mspace{14mu} 1},2}\left( {t_{1} - t_{0}} \right)}\left( {{cdi}_{1} - {a_{4}{cbi}_{0}}} \right)}{{cdi}_{1} - {cdi}_{0}} \right)}} & (25)\end{matrix}$

Experiments have shown that the measuring accuracy is high particularlywhen the blood and dialyzing-fluid flow Qb, Qd are high.

1. A method for determining the distribution volume of a blood componentin the body of an organism during an extracorporeal blood treatment, inwhich the blood to be treated flows in an extracorporeal circuit throughthe blood chamber of a dialyzer subdivided by a semipermeable membraneinto the blood chamber and a dialyzing-fluid chamber, and dialyzingfluid flows in a dialyzing-fluid path through the dialyzing-fluidchamber of the dialyzer, comprising the following method steps: bringingabout a change in the concentration of the blood component in the bloodupstream of the dialyzer by a change in the concentration of the bloodcomponent in the dialyzing fluid upstream of the dialyzer; and measuringthe change in the concentration of the blood component in the dialyzingfluid downstream of the dialyzer which can be attributed to the changein the concentration of the blood component in the blood as a result ofthe change in the concentration of the blood component in the dialyzingfluid upstream of the dialyzer; and determining the distribution volumeV of the blood component from the change in the concentration of theblood component in the dialyzing fluid upstream and downstream of thedialyzer.
 2. The method as recited in claim 1, wherein the concentrationof the blood component in the dialyzing fluid in the dialyzing-fluidpath is measured upstream of the dialyzer.
 3. The method as recited inclaim 1, wherein the conductivity of the dialyzing fluid is measured asthe concentration of the blood component for determining thedistribution volume of sodium in the blood.
 4. The method as recited inclaim 3, wherein the sodium distribution volume is ascertained fordetermining the distribution volume of urea in the blood, and the ureadistribution volume is determined from the sodium distribution volume.5. The method as recited in claim 4, wherein the urea distributionvolume is determined under the assumption that the sodium distributionvolume essentially corresponds to the urea distribution volume.
 6. Amethod for determining the distribution volume of a blood component inthe body of an organism during an extracorporeal blood treatment, inwhich the blood to be treated flows in an extracorporeal circuit throughthe blood chamber of a dialyzer subdivided by a semipermeable membraneinto the blood chamber and a dialyzing-fluid chamber, and dialyzingfluid flows in a dialyzing-fluid path through the dialyzing-fluidchamber of the dialyzer, comprising the following method steps: theconcentration of the blood component in the dialyzing fluid is alteredin the dialyzing-fluid path upstream of the dialyzer and theconcentration of the blood component in the dialyzing fluid is measureddownstream of the dialyzer; the change as a function of time in theconcentration of a blood component in the blood upstream of the dialyzerΔcbi as a result of the change in the concentration of the bloodcomponent in the dialyzing fluid upstream of the dialyzer is determinedfrom the concentration of the blood component in the dialyzing fluidupstream and downstream of the dialyzer after the concentration of theblood component in the dialyzing fluid has been altered; and thedistribution volume V of the blood component is determined from thechange as a function of time in the concentration of the blood componentin the blood.
 7. The method as recited in claim 6, wherein theconcentration of the blood component in the dialyzing fluid in thedialyzing-fluid path is measured upstream of the dialyzer.
 8. A methodfor determining the distribution volume of a blood component in the bodyof an organism during an extracorporeal blood treatment, in which theblood to be treated flows in an extracorporeal circuit through the bloodchamber of a dialyzer subdivided by a semipermeable membrane into theblood chamber and a dialyzing-fluid chamber, and dialyzing fluid flowsin a dialyzing-fluid path through the dialyzing-fluid chamber of thedialyzer, comprising the following method steps: bringing about a changein the concentration of a blood component in the blood upstream of thedialyzer by a change in a physical or chemical characteristic in thedialyzing fluid upstream of the dialyzer; and measuring the change inthe physical or chemical characteristic in the dialyzing fluiddownstream of the dialyzer which can be attributed to the change in theconcentration of the blood component in the blood; and determining thedistribution volume V of the blood component from the change in thephysical or chemical characteristic in the dialyzing fluid upstream anddownstream of the dialyzer, wherein the physical or chemicalcharacteristic of the dialyzing fluid in the dialyzing-fluid path isincreased at a point of time t₀ from a predetermined first value cdi₀ toa predetermined second value cdi₁, is reduced at a point of time t₁>t₀to a predetermined third value cdi₂, and is increased at a point of timet₂>t₁ to a predetermined fourth value cdi₀ which is equal to the firstvalue, the value by which the characteristic is increased being half aslarge as the value by which the characteristic is reduced.
 9. The methodas recited in claim 8, wherein the time interval t₁−t₀ is equal to thetime interval t₂−t₁.
 10. The method as recited in claim 8, wherein thechange as a function of time in the concentration of a blood componentin the blood upstream of the dialyzer Δcbi is ascertained from: thepredetermined first value cdi₀ of the physical or chemicalcharacteristic of the dialyzing fluid upstream of the dialyzer and thevalue cdo₀ of the characteristic that ensues downstream of the dialyzer,and the predetermined second value cdi₁ of the characteristic upstreamof the dialyzer and the value cdo₁ of the characteristic which ensuesdownstream of the dialyzer after the increase in the characteristicupstream of the dialyzer to the predetermined second value, and thepredetermined third value cdi₂ of the characteristic upstream of thedialyzer and the value cdo₂ of the characteristic which ensuesdownstream of the dialyzer after the decrease in the characteristicupstream of the dialyzer to the predetermined third value.
 11. Themethod as recited in claim 10, wherein the dialyzing fluid is balancedsuch that the volume of the dialyzing fluid flowing into the dialyzerduring the measurement is equal to the volume of the dialyzing fluidflowing out of the dialyzer.
 12. An apparatus for determining thedistribution volume of a blood component in the body of an organismduring an extracorporeal blood treatment in conjunction with anextracorporeal blood-treatment device, in which the blood to be treatedflows in an extracorporeal circuit through the blood chamber of adialyzer subdivided by a semipermeable membrane into the blood chamberand a dialyzing-fluid chamber, and dialyzing fluid flows in adialyzing-fluid path through the dialyzing-fluid chamber of thedialyzer, having a device configured to alter the concentration of theblood component in the dialyzing fluid in the dialyzing-fluid pathupstream of the dialyzer, and a measuring device configured to determinethe concentration of the blood component in the dialyzing fluid in thedialyzing-fluid path downstream of the dialyzer, wherein the apparatuscomprises an arithmetic and evaluation configured in such a way that thedistribution volume V of the blood component can be determined from achange in the concentration of the blood component in the dialyzingfluid downstream of the dialyzer which can be attributed to the changein the concentration of the blood component in the blood as a result ofthe change in the concentration of the blood component in the dialyzingfluid upstream of the dialyzer.
 13. The apparatus as recited in claim12, wherein a measuring device is provided for detecting theconcentration of the blood component in the dialyzing fluid in thedialyzing-fluid path upstream of the dialyzer.
 14. The apparatus asrecited in claim 13, wherein the measuring devices for detecting theconcentration of the blood component have a conductivity sensor, opticalsensor or enzyme sensor arranged in the dialyzing-fluid path downstreamand upstream, respectively, of the dialyzer.
 15. The apparatus asrecited in claim 12, wherein the device for altering the concentrationof the blood component is designed in such a way that the concentrationof the blood component is increased at a point of time t₀ from apredetermined first value cdi₀ to a predetermined second value cdi₁, isreduced at a point of time t₁>t₀ to a predetermined third value cdi₂,and is increased at a point of time t₂>μt₁ to a predetermined fourthvalue cdi₀ which is equal to the first value, the value by which theconcentration of the blood component is increased being half as large asthe value by which the concentration of the blood component is reduced.16. The apparatus as recited in claim 15, wherein the time intervalt₁−t₀ is equal to the time interval t₂−t₁.
 17. The apparatus as recitedin claim 15, wherein the arithmetic and evaluation unit is designed insuch a way that the predetermined first, second and third values cdi₀,cdi₁, cdi₂ of the concentration of the blood component in the dialyzingfluid upstream of the dialyzer and the values cdo₀, cdo₁, cdo₂ of theconcentration of the blood component in the dialyzing fluid ensuingdownstream of the dialyzer are evaluable for determining the change as afunction of time in the concentration of the blood component Δcbi. 18.The apparatus as recited in claim 12, wherein a balancing device isprovided with which the dialyzing fluid can be balanced in such a waythat the volume of the dialyzing fluid flowing into the dialyzer duringthe measurement is equal to the volume of the dialyzing fluid flowingout of the dialyzer.
 19. An apparatus for determining the distributionvolume of a blood component in the body of an organism during anextracorporeal blood treatment in conjunction with an extracorporealblood-treatment device, in which the blood to be treated flows in anextracorporeal circuit through the blood chamber of a dialyzersubdivided by a semipermeable membrane into the blood chamber and adialyzing-fluid chamber, and dialyzing fluid flows in a dialyzing-fluidpath through the dialyzing-fluid chamber of the dialyzer, having adevice configured to alter the concentration of the blood component inthe dialyzing fluid in the dialyzing-fluid path upstream of thedialyzer, and a measuring device configured to determine theconcentration of the blood component in the dialyzing fluid in thedialyzing-fluid path downstream of the dialyzer, wherein the apparatuscomprises an arithmetic and evaluation configured in such a way that thechange as a function of time in the concentration of the blood componentΔcbi in the blood upstream of the dialyzer as a result of the change inthe concentration of the blood component in the dialyzing fluid upstreamof the dialyzer can be determined from the concentration of the bloodcomponent in the dialyzing fluid upstream and downstream of the dialyzerafter the concentration of the blood component in the dialyzing fluidhas been altered, and the distribution volume V of the blood componentcan be determined from the change as a function of time in theconcentration of the blood component upstream of the dialyzer.
 20. Theapparatus as recited in claim 19, wherein a measuring device is providedfor detecting the concentration of the blood component in the dialyzingfluid in the dialyzing-fluid path upstream of the dialyzer.
 21. Theapparatus as recited in claim 19, wherein the device for altering theconcentration of the blood component is designed in such a way that theconcentration of the blood component is increased at a point of time t₀from a predetermined first value cdi₀ to a predetermined second valuecdi₁, is reduced at a point of time t₁>t₀ to a predetermined third valuecdi₂, and is increased at a point of time t₂>t₁ to a predeterminedfourth value cdi₀ which is equal to the first value, the value by whichthe concentration of the blood component is increased being half aslarge as the value by which the concentration of the blood component isreduced.
 22. The apparatus as recited in claim 19, wherein thearithmetic and evaluation unit is designed in such a way that thepredetermined first, second and third values cdi₀, cdi₁, cdi₂ of theconcentration of the blood component in the dialyzing fluid upstream ofthe dialyzer and the values cdo₀, cdo₁, cdo₂ of the concentration of theblood component in the dialyzing fluid ensuing downstream of thedialyzer are evaluable for determining the change as a function of timein the concentration of the blood component Δcbi.
 23. The apparatus asrecited in claim 19, wherein a balancing device is provided with whichthe dialyzing fluid can be balanced in such a way that the volume of thedialyzing fluid flowing into the dialyzer during the measurement isequal to the volume of the dialyzing fluid flowing out of the dialyzer.24. A method for determining the distribution volume of a bloodcomponent in the body of an organism during an extracorporeal bloodtreatment, in which the blood to be treated flows in an extracorporealcircuit through the blood chamber of a dialyzer subdivided by asemipermeable membrane into the blood chamber and a dialyzing-fluidchamber, and dialyzing fluid flows in a dialyzing-fluid path through thedialyzing-fluid chamber of the dialyzer, comprising the following methodsteps: a physical or chemical characteristic of the dialyzing fluid isaltered in the dialyzing-fluid path upstream of the dialyzer, and thephysical or chemical characteristic of the dialyzing fluid is measureddownstream of the dialyzer; the change as a function of time in theconcentration of a blood component in the blood upstream of the dialyzerΔcbi is determined from the physical or chemical characteristic of thedialyzing fluid upstream and downstream of the dialyzer; and thedistribution volume V of the blood component is determined from thechange as a function of time in the concentration of a blood componentin the blood, wherein the physical or chemical characteristic of thedialyzing fluid in the dialyzing-fluid path is increased at a point oftime t₀ from a predetermined first value cdi₀ to a predetermined secondvalue cdi₁, is reduced at a point of time t₁>t₀ to a predetermined thirdvalue cdi₂, and is increased at a point of time t₂>t₁ to a predeterminedfourth value cdi₀ which is equal to the first value, the value by whichthe characteristic is increased being half as large as the value bywhich the characteristic is reduced.
 25. The method as recited in claim24, wherein the change as a function of time in the concentration of ablood component in the blood upstream of the dialyzer Δcbi isascertained from: the predetermined first value cdi₀ of the physical orchemical characteristic of the dialyzing fluid upstream of the dialyzerand the value cdo₀ of the characteristic that ensues downstream of thedialyzer, and the predetermined second value cdi₁ of the characteristicupstream of the dialyzer and the value cdo₁ of the characteristic whichensues downstream of the dialyzer after the increase in thecharacteristic upstream of the dialyzer to the predetermined secondvalue, and the predetermined third value cdi₂ of the characteristicupstream of the dialyzer and the value cdo₂ of the characteristic whichensues downstream of the dialyzer after the decrease in thecharacteristic upstream of the dialyzer to the predetermined thirdvalue.